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Home Equity worksheet

Grades 11–12 · CCSS HSA.SSE.B.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

  1. Problem 1.
    • Current home value: $450,000
    • Mortgage balance owed: $260,000
    • Maximum combined loan-to-value: 100%
    • Amount you want to borrow: $38,000
    • Type of borrowing: Line of credit (HELOC)
    • Interest rate: 7.5% per year
    • Draw period (interest only): 7 years
    • Repayment period: 18 years

    Find: Maximum you could borrow

  2. Problem 2.
    • Current home value: $660,000
    • Mortgage balance owed: $225,000
    • Maximum combined loan-to-value: 90%
    • Amount you want to borrow: $36,000
    • Type of borrowing: Line of credit (HELOC)
    • Interest rate: 8% per year
    • Draw period (interest only): 11 years
    • Repayment period: 20 years

    Find: Maximum you could borrow

  3. Problem 3.
    • Current home value: $460,000
    • Mortgage balance owed: $160,000
    • Maximum combined loan-to-value: 80%
    • Amount you want to borrow: $45,000
    • Type of borrowing: Home equity loan (fixed payments)
    • Interest rate: 9.25% per year
    • Loan term: 5 years

    Find: Maximum you could borrow

  4. Problem 4.
    • Current home value: $360,000
    • Mortgage balance owed: $220,000
    • Maximum combined loan-to-value: 100%
    • Amount you want to borrow: $45,000
    • Type of borrowing: Home equity loan (fixed payments)
    • Interest rate: 7% per year
    • Loan term: 15 years

    Find: Maximum you could borrow

  5. Problem 5.
    • Current home value: $450,000
    • Mortgage balance owed: $235,000
    • Maximum combined loan-to-value: 100%
    • Amount you want to borrow: $42,000
    • Type of borrowing: Home equity loan (fixed payments)
    • Interest rate: 8.5% per year
    • Loan term: 15 years

    Find: Maximum you could borrow

  6. Problem 6.
    • Current home value: $440,000
    • Mortgage balance owed: $160,000
    • Maximum combined loan-to-value: 100%
    • Amount you want to borrow: $50,000
    • Type of borrowing: Home equity loan (fixed payments)
    • Interest rate: 5.5% per year
    • Loan term: 10 years

    Find: Maximum you could borrow

  7. Problem 7.
    • Current home value: $500,000
    • Mortgage balance owed: $240,000
    • Maximum combined loan-to-value: 100%
    • Amount you want to borrow: $41,000
    • Type of borrowing: Home equity loan (fixed payments)
    • Interest rate: 10% per year
    • Loan term: 20 years

    Find: Maximum you could borrow

  8. Problem 8.
    • Current home value: $460,000
    • Mortgage balance owed: $275,000
    • Maximum combined loan-to-value: 80%
    • Amount you want to borrow: $45,000
    • Type of borrowing: Line of credit (HELOC)
    • Interest rate: 9.5% per year
    • Draw period (interest only): 7 years
    • Repayment period: 22 years

    Find: Maximum you could borrow

  9. Problem 9.
    • Current home value: $425,000
    • Mortgage balance owed: $225,000
    • Maximum combined loan-to-value: 100%
    • Amount you want to borrow: $39,000
    • Type of borrowing: Home equity loan (fixed payments)
    • Interest rate: 8.5% per year
    • Loan term: 10 years

    Find: Maximum you could borrow

  10. Problem 10.
    • Current home value: $500,000
    • Mortgage balance owed: $280,000
    • Maximum combined loan-to-value: 90%
    • Amount you want to borrow: $60,000
    • Type of borrowing: Line of credit (HELOC)
    • Interest rate: 7.25% per year
    • Draw period (interest only): 10 years
    • Repayment period: 22 years

    Find: Maximum you could borrow

Answer key: Home Equity worksheet

  1. 1. Maximum you could borrow: $190,000.00

    1. Equity: the home's value minus what you owe on it

      $450,000.00−$260,000.00=$190,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $260,000.00$450,000.00=57.78%
    3. The lender caps all loans on the home at 100% of its value. Subtract what you already owe to see how much room is left

      $450,000.00×100%−$260,000.00=$190,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $260,000.00+$38,000.00$450,000.00=66.22%
    5. While you can draw on the line, you pay only one month's interest: the balance × the yearly rate ÷ 12

      $38,000.00×7.5%12=$237.50
    6. When the draw period ends, the whole balance is paid off in 216 equal monthly payments, with interest

      $38,000.00×0.006251−(1+0.00625)−216=$321.09
    7. Add the interest-only payments from the draw period to the interest paid during repayment

      $237.50×84+$321.09×216−$38,000.00=$51,305.41
  2. 2. Maximum you could borrow: $369,000.00

    1. Equity: the home's value minus what you owe on it

      $660,000.00−$225,000.00=$435,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $225,000.00$660,000.00=34.09%
    3. The lender caps all loans on the home at 90% of its value. Subtract what you already owe to see how much room is left

      $660,000.00×90%−$225,000.00=$369,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $225,000.00+$36,000.00$660,000.00=39.55%
    5. While you can draw on the line, you pay only one month's interest: the balance × the yearly rate ÷ 12

      $36,000.00×8%12=$240.00
    6. When the draw period ends, the whole balance is paid off in 240 equal monthly payments, with interest

      $36,000.00×0.006666671−(1+0.00666667)−240=$301.12
    7. Add the interest-only payments from the draw period to the interest paid during repayment

      $240.00×132+$301.12×240−$36,000.00=$67,948.42
  3. 3. Maximum you could borrow: $208,000.00

    1. Equity: the home's value minus what you owe on it

      $460,000.00−$160,000.00=$300,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $160,000.00$460,000.00=34.78%
    3. The lender caps all loans on the home at 80% of its value. Subtract what you already owe to see how much room is left

      $460,000.00×80%−$160,000.00=$208,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $160,000.00+$45,000.00$460,000.00=44.57%
    5. Find the monthly payment. A standard formula gives the one amount that pays off $45,000.00 in 60 equal months, at the monthly rate i (the yearly rate ÷ 12)

      $45,000.00×0.007708331−(1+0.00770833)−60=$939.60
    6. Total interest: all the payments minus the amount borrowed

      $939.60×60−$45,000.00=$11,375.73
  4. 4. Maximum you could borrow: $140,000.00

    1. Equity: the home's value minus what you owe on it

      $360,000.00−$220,000.00=$140,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $220,000.00$360,000.00=61.11%
    3. The lender caps all loans on the home at 100% of its value. Subtract what you already owe to see how much room is left

      $360,000.00×100%−$220,000.00=$140,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $220,000.00+$45,000.00$360,000.00=73.61%
    5. Find the monthly payment. A standard formula gives the one amount that pays off $45,000.00 in 180 equal months, at the monthly rate i (the yearly rate ÷ 12)

      $45,000.00×0.005833331−(1+0.00583333)−180=$404.47
    6. Total interest: all the payments minus the amount borrowed

      $404.47×180−$45,000.00=$27,805.09
  5. 5. Maximum you could borrow: $215,000.00

    1. Equity: the home's value minus what you owe on it

      $450,000.00−$235,000.00=$215,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $235,000.00$450,000.00=52.22%
    3. The lender caps all loans on the home at 100% of its value. Subtract what you already owe to see how much room is left

      $450,000.00×100%−$235,000.00=$215,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $235,000.00+$42,000.00$450,000.00=61.56%
    5. Find the monthly payment. A standard formula gives the one amount that pays off $42,000.00 in 180 equal months, at the monthly rate i (the yearly rate ÷ 12)

      $42,000.00×0.007083331−(1+0.00708333)−180=$413.59
    6. Total interest: all the payments minus the amount borrowed

      $413.59×180−$42,000.00=$32,446.31
  6. 6. Maximum you could borrow: $280,000.00

    1. Equity: the home's value minus what you owe on it

      $440,000.00−$160,000.00=$280,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $160,000.00$440,000.00=36.36%
    3. The lender caps all loans on the home at 100% of its value. Subtract what you already owe to see how much room is left

      $440,000.00×100%−$160,000.00=$280,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $160,000.00+$50,000.00$440,000.00=47.73%
    5. Find the monthly payment. A standard formula gives the one amount that pays off $50,000.00 in 120 equal months, at the monthly rate i (the yearly rate ÷ 12)

      $50,000.00×0.004583331−(1+0.00458333)−120=$542.63
    6. Total interest: all the payments minus the amount borrowed

      $542.63×120−$50,000.00=$15,115.77
  7. 7. Maximum you could borrow: $260,000.00

    1. Equity: the home's value minus what you owe on it

      $500,000.00−$240,000.00=$260,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $240,000.00$500,000.00=48%
    3. The lender caps all loans on the home at 100% of its value. Subtract what you already owe to see how much room is left

      $500,000.00×100%−$240,000.00=$260,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $240,000.00+$41,000.00$500,000.00=56.2%
    5. Find the monthly payment. A standard formula gives the one amount that pays off $41,000.00 in 240 equal months, at the monthly rate i (the yearly rate ÷ 12)

      $41,000.00×0.008333331−(1+0.00833333)−240=$395.66
    6. Total interest: all the payments minus the amount borrowed

      $395.66×240−$41,000.00=$53,958.13
  8. 8. Maximum you could borrow: $93,000.00

    1. Equity: the home's value minus what you owe on it

      $460,000.00−$275,000.00=$185,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $275,000.00$460,000.00=59.78%
    3. The lender caps all loans on the home at 80% of its value. Subtract what you already owe to see how much room is left

      $460,000.00×80%−$275,000.00=$93,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $275,000.00+$45,000.00$460,000.00=69.57%
    5. While you can draw on the line, you pay only one month's interest: the balance × the yearly rate ÷ 12

      $45,000.00×9.5%12=$356.25
    6. When the draw period ends, the whole balance is paid off in 264 equal monthly payments, with interest

      $45,000.00×0.007916671−(1+0.00791667)−264=$407.01
    7. Add the interest-only payments from the draw period to the interest paid during repayment

      $356.25×84+$407.01×264−$45,000.00=$92,375.01
  9. 9. Maximum you could borrow: $200,000.00

    1. Equity: the home's value minus what you owe on it

      $425,000.00−$225,000.00=$200,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $225,000.00$425,000.00=52.94%
    3. The lender caps all loans on the home at 100% of its value. Subtract what you already owe to see how much room is left

      $425,000.00×100%−$225,000.00=$200,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $225,000.00+$39,000.00$425,000.00=62.12%
    5. Find the monthly payment. A standard formula gives the one amount that pays off $39,000.00 in 120 equal months, at the monthly rate i (the yearly rate ÷ 12)

      $39,000.00×0.007083331−(1+0.00708333)−120=$483.54
    6. Total interest: all the payments minus the amount borrowed

      $483.54×120−$39,000.00=$19,025.30
  10. 10. Maximum you could borrow: $170,000.00

    1. Equity: the home's value minus what you owe on it

      $500,000.00−$280,000.00=$220,000.00
    2. Current loan-to-value: what you owe as a share of the value

      $280,000.00$500,000.00=56%
    3. The lender caps all loans on the home at 90% of its value. Subtract what you already owe to see how much room is left

      $500,000.00×90%−$280,000.00=$170,000.00
    4. Check the combined loan-to-value after borrowing: everything you'd owe as a share of the value

      $280,000.00+$60,000.00$500,000.00=68%
    5. While you can draw on the line, you pay only one month's interest: the balance × the yearly rate ÷ 12

      $60,000.00×7.25%12=$362.50
    6. When the draw period ends, the whole balance is paid off in 264 equal monthly payments, with interest

      $60,000.00×0.006041671−(1+0.00604167)−264=$455.34
    7. Add the interest-only payments from the draw period to the interest paid during repayment

      $362.50×120+$455.34×264−$60,000.00=$103,708.70